A ‘stack’ model of rate-independent polycrystals. (English) Zbl 1426.74066
Summary: A novel ‘stack’ model of a rate-independent polycrystal, which extends the ‘ALAMEL’ model of P. Van Houtte et al. [ibid. 21, No. 3, 589–624 (2005; Zbl 1154.74320)] is proposed. In the ‘stack’ model, stacks of \(N\) neighboring ‘ALAMEL’ domains collectively accommodate the imposed macroscopic deformation while deforming such that velocity and traction continuity with their neighbors is maintained. The flow law and consistency conditions are derived and an efficient solution methodology based on the linear programming technique is given. The present model is applied to study plastic deformation of an idealized two-dimensional polycrystal under macroscopically imposed plane-strain tension and simple shear constraints. Qualitative and quantitative variations in the predicted macroscopic and microscopic response with \(N\) are presented. The constraint on individual ‘ALAMEL’ domains diminishes with stack size \(N\) but saturates for large \(N\). Computational effort associated with the present model is analyzed and found to be well within one order of magnitude greater than that required to solve the classical Taylor model. Furthermore, implementation of the consistency conditions is found to reduce computation time by at least 50%.
MSC:
| 74C15 | Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) |
| 74E15 | Crystalline structure |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 90C90 | Applications of mathematical programming |
Keywords:
crystal plasticity; polycrystal model; flow law; consistency conditions; linear programmingCitations:
Zbl 1154.74320Software:
LSODEReferences:
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